dCS 904 User Manual | Manual for Software Version 1.5x and 1.36 |
dCS Ltd | June 2000 |
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GENERAL TECHNICAL INFORMATION
Word Length Reduction
Word length reduction (truncation) causes an error signal to be added to the wanted signal. The error signal is usually referred to as “Q noise” or Quantisation noise – the approximation is usually made that the errors are noise like. This is reasonably true for large signals, where the errors are very complex if they are not exactly noise like. Importantly, though, for smaller ones it is not so. As the wanted signal gets smaller, the complexity of the error signal decreases. The errors first of all pile into ever fewer lower order harmonics or intermods, and then, as the level of the signal sinks below the Q level, the majority of the error power piles into the signal fundamental. This causes its amplitude to become unpredictable – it may drop abruptly to zero and disappear, or it may cease to go down any more and just stay at a constant level. From the audio viewpoint, this sounds very unpleasant. As a signal tail decays away, the tonal quality changes, and then it decays into distorted mush and then either abruptly stops, or else keeps fuzzing away until a new signal starts. The level at which all this happens is the lsb of the output word – for CDs, it is at the 16 bit level, which equates to about
There is really only one way of tackling the problem – another signal has to be added to the wanted one to smooth the staircase transfer function that truncation causes. Mathematically, with two signals present, the transfer function that the wanted signal sees is the convolution of the PDF10 of the second signal and the staircase function. The converse is also true – the transfer function the additional signal sees is the convolution of the PDF of the wanted signal and the staircase function. This aspect is not a problem with the dither types considered below, but it can be with some highly frequency shaped dithers.
The trick is to make the second signal as inaudible as possible. It is usually referred to as dither, and it is usually noise like, because then its statistics can be controlled, and the converse effect of the signal modulating the dither can be made insignificant, or zero. However, there are a number of ways that this dither signal can be generated and treated. The major options are:
•generate it from the signal or generate it independently and add it (“Dither”). It seems implausible that the dither signal can be generated from the signal, but it can, and this gives the lowest added noise power option. It is noise shaping on its own, but there are some circumstances where it needs help from additional dither.
•add inside or outside an error shaping loop
•frequency shape to match the ears response or not. One can use techniques that suppress error energy in the areas where the ear is sensitive, and put it in areas where the ear is not sensitive. Usually this shuffling around process costs something – we remove a little from the sensitive areas and add back rather more in the less sensitive parts, but that’s life. We still gain some improvements.
The table below gives the actual noise levels for 16 bit truncated signals with no dither, various types of dither, noise shaping on its own, and noise shaping with dither. The 0 dB reference level is taken as the minimum noise we could
10PDF = Probability Distribution Function. References to Rectangular Dither or Triangular Dither refer the shape of the PDF of the dither.
Manual part no: DOC135904 iss 2B2 | Page 64 | 135904ma2b2.pdf file available from website |
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